Bring the chicken stock to a boil, stir in the rice and reduce the heat to a simmer. Cover and cook for 40-45 minutes, until the wild rice blooms and is tender. Drain and cool on a baking sheet, then transfer to a mixing bowl.
In a skillet, heat the EVOO over medium-high heat, a turn of the pan. Melt in the butter, then add the mushrooms and sauté to soften, 5-6 minutes. Add the leek, thyme and dill; season with salt and pepper. Cook for 3-4 minutes more; deglaze with the vermouth or wine. Add the lemon juice and transfer to the mixing bowl with rice. Stir to combine.
Pre-heat the oven to 425°F. Cover a baking sheet with parchment paper.
Gently roll out the puff pastry sheet with a sprinkle of flour. Cut four rectangles about 6×8 inches.
Heat a drizzle of EVOO in large, nonstick skillet over medium-high heat. Season the salmon fillets with salt and pepper and add them to the hot pan. Brown the fish for 2 minutes on the first side and 1 minute on the flip side. Remove from the heat.
Pile some rice and mushroom topping onto each pastry rectangle in small even mounds, leaving an edge all around for wrapping. Place a piece of salmon on top. Wrap and seal the bundles of salmon and set them on the baking sheet. Brush with egg wash.
Bake for 15 minutes, or until deeply golden. Serve with Beurre Blanc (optional) and asparagus or haricots verts alongside.